A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10^{−27} kg.v

#### Solution

Given:

Mass of neutron, *m* = 1.67 × 10^{−27} kg

Since neutron is moving with velocity (v), its energy (E) is given by

`E = 1/2 mv ^2`

Let the energy absorbed be ∆*E**.*

The condition for inelastic collision is given below:

`1/2mv^2 > 2 Delta E`

`rArr DeltaE < 1/4 mv^2`

Since 10.2 eV, energy is required for the first excited state.

`therefore DeltaE < 10.2 eV `

`therefore 10.2 eV < 1/4 mv^2`

Thus, minimum speed of the neutron is given by

`rArr v_min = sqrt((4xx10.2)/m eV`

`rArr v_min = sqrt((10.2xx1.6xx10^19xx4)/(1.67xx10^-27)`

= 6 × 10^{4 }m/sec